Details

analyze1.2s (10.5%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
25%	74.9%	0.1%	6
25%	74.9%	0.1%	7
25%	74.9%	0.1%	8
25%	74.9%	0.1%	9
25%	64%	11.1%	10
31.2%	54.6%	14.2%	11
39%	44.1%	16.9%	12
39%	41.5%	19.5%	13
42.9%	37%	20.1%	14

Compiler

Compiled 23 to 16 computations (30.4% saved)

sample4.8s (41.5%)

Symmetry

(sort a1 a2)

Results

1.4s	1845×	body	1024	valid
1.2s	1578×	body	1024	invalid
959.0ms	4985×	body	128	valid
498.0ms	955×	body	512	valid
383.0ms	781×	body	512	invalid
153.0ms	466×	body	256	valid
145.0ms	412×	body	256	invalid
132.0ms	666×	body	128	invalid
6.0ms	5×	body	2048	valid

Compiler

Compiled 68 to 47 computations (30.9% saved)

simplify9.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

32×	`fma-def_binary64`
23×	`*-commutative_binary64`
20×	`associate-/l*_binary64`
11×	`associate-/r/_binary64`
9×	`associate-*r/_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	20
1	27	18
2	53	18
3	76	18
4	103	18
5	117	18
6	132	18
7	134	18
8	136	18
9	136	18

prune4.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Kept	Total
New	2	2
Fresh	1	1
Picked	0	0
Done	0	0
Total	3	3

Error

0.6b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.7b	(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))
	0.7b	(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))

Compiler

Compiled 108 to 70 computations (35.2% saved)

localize9.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))
✓	0.6b	(/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 2))

series94.0ms (0.8%)

Counts

2 → 60

Calls

2 calls:

63.0ms	(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))
31.0ms	(/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 2))

rewrite17.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

39×	`add-sqr-sqrt_binary64`
38×	`times-frac_binary64`
31×	`*-un-lft-identity_binary64`
31×	`add-cube-cbrt_binary64`
22×	`associate-r_binary64`

Counts

2 → 85

Calls

2 calls:

7.0ms	(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))
3.0ms	(/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 2))

simplify111.0ms (1%)

Algorithm

1×	egg-herbie

Rules

456×	`associate-l_binary64`
410×	`associate-r_binary64`
396×	`fma-neg_binary64`
332×	`associate-/l*_binary64`
299×	`sub-neg_binary64`

Counts

145 → 151

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	170	3315
1	365	3012
2	1289	2968
3	4359	2968
4	5076	2968

prune147.0ms (1.3%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	144	7	151
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	145	8	153

Error

Counts

153 → 8

Alt Table

Status	Error	Program
	0.8b	(.f64 (/.f64 (cos.f64 th) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (cbrt.f64 (sqrt.f64 2))))
	15.8b	(.f64 (sqrt.f64 (cos.f64 th)) (.f64 (sqrt.f64 (cos.f64 th)) (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 2))))
	0.6b	(.f64 (cos.f64 th) (.f64 (/.f64 (hypot.f64 a2 a1) (sqrt.f64 (sqrt.f64 2))) (/.f64 (hypot.f64 a2 a1) (sqrt.f64 (sqrt.f64 2)))))
	0.8b	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 (sqrt.f64 2))) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2))))
▶	0.4b	(.f64 (cos.f64 th) (.f64 (/.f64 (hypot.f64 a2 a1) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (/.f64 (hypot.f64 a2 a1) (cbrt.f64 (sqrt.f64 2)))))
	0.7b	(.f64 (cos.f64 th) (/.f64 (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2))))
	0.7b	(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))
	1.5b	(.f64 (.f64 (cbrt.f64 (.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))) (cbrt.f64 (.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2))))) (cbrt.f64 (.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))))

Compiler

Compiled 3809 to 1808 computations (52.5% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (hypot.f64 a2 a1) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))))
✓	0.2b	(.f64 (cos.f64 th) (.f64 (/.f64 (hypot.f64 a2 a1) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (/.f64 (hypot.f64 a2 a1) (cbrt.f64 (sqrt.f64 2)))))
✓	0.2b	(/.f64 (hypot.f64 a2 a1) (cbrt.f64 (sqrt.f64 2)))
✓	0.3b	(.f64 (/.f64 (hypot.f64 a2 a1) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (/.f64 (hypot.f64 a2 a1) (cbrt.f64 (sqrt.f64 2))))

series300.0ms (2.6%)

Counts

4 → 108

Calls

4 calls:

120.0ms	(.f64 (cos.f64 th) (.f64 (/.f64 (hypot.f64 a2 a1) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (/.f64 (hypot.f64 a2 a1) (cbrt.f64 (sqrt.f64 2)))))
71.0ms	(/.f64 (hypot.f64 a2 a1) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))))
66.0ms	(.f64 (/.f64 (hypot.f64 a2 a1) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (/.f64 (hypot.f64 a2 a1) (cbrt.f64 (sqrt.f64 2))))
43.0ms	(/.f64 (hypot.f64 a2 a1) (cbrt.f64 (sqrt.f64 2)))

rewrite59.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

72×	`add-sqr-sqrt_binary64`
70×	`times-frac_binary64`
61×	`add-exp-log_binary64`
50×	`*-un-lft-identity_binary64`
50×	`add-cube-cbrt_binary64`

Counts

4 → 181

Calls

4 calls:

15.0ms	(.f64 (/.f64 (hypot.f64 a2 a1) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (/.f64 (hypot.f64 a2 a1) (cbrt.f64 (sqrt.f64 2))))
14.0ms	(.f64 (cos.f64 th) (.f64 (/.f64 (hypot.f64 a2 a1) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (/.f64 (hypot.f64 a2 a1) (cbrt.f64 (sqrt.f64 2)))))
6.0ms	(/.f64 (hypot.f64 a2 a1) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))))
3.0ms	(/.f64 (hypot.f64 a2 a1) (cbrt.f64 (sqrt.f64 2)))

simplify187.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

517×	`cancel-sign-sub-inv_binary64`
363×	`fma-neg_binary64`
266×	`associate-r_binary64`
250×	`associate-l_binary64`
250×	`associate-*r/_binary64`

Counts

289 → 309

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	347	9877
1	938	7509
2	3617	7422
3	5079	7422

prune382.0ms (3.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	308	1	309
Fresh	1	6	7
Picked	0	1	1
Done	0	0	0
Total	309	8	317

Error

Counts

317 → 8

Alt Table

Status	Error	Program
	0.8b	(.f64 (/.f64 (cos.f64 th) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (cbrt.f64 (sqrt.f64 2))))
	15.8b	(.f64 (sqrt.f64 (cos.f64 th)) (.f64 (sqrt.f64 (cos.f64 th)) (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 2))))
	0.6b	(.f64 (cos.f64 th) (.f64 (/.f64 (hypot.f64 a2 a1) (sqrt.f64 (sqrt.f64 2))) (/.f64 (hypot.f64 a2 a1) (sqrt.f64 (sqrt.f64 2)))))
	0.8b	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 (sqrt.f64 2))) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2))))
✓	0.4b	(.f64 (cos.f64 th) (.f64 (/.f64 (hypot.f64 a2 a1) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (/.f64 (hypot.f64 a2 a1) (cbrt.f64 (sqrt.f64 2)))))
	0.7b	(.f64 (cos.f64 th) (/.f64 (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2))))
	0.7b	(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))
▶	0.5b	(*.f64 (cos.f64 th) (pow.f64 (/.f64 (hypot.f64 a2 a1) (/.f64 (sqrt.f64 2) (hypot.f64 a2 a1))) 1))

Compiler

Compiled 10532 to 6913 computations (34.4% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(hypot.f64 a2 a1)
✓	0.2b	(*.f64 (cos.f64 th) (pow.f64 (/.f64 (hypot.f64 a2 a1) (/.f64 (sqrt.f64 2) (hypot.f64 a2 a1))) 1))
✓	0.2b	(/.f64 (hypot.f64 a2 a1) (/.f64 (sqrt.f64 2) (hypot.f64 a2 a1)))
✓	0.5b	(/.f64 (sqrt.f64 2) (hypot.f64 a2 a1))

series213.0ms (1.8%)

Counts

4 → 108

Calls

4 calls:

110.0ms	(*.f64 (cos.f64 th) (pow.f64 (/.f64 (hypot.f64 a2 a1) (/.f64 (sqrt.f64 2) (hypot.f64 a2 a1))) 1))
65.0ms	(/.f64 (hypot.f64 a2 a1) (/.f64 (sqrt.f64 2) (hypot.f64 a2 a1)))
24.0ms	(/.f64 (sqrt.f64 2) (hypot.f64 a2 a1))
14.0ms	(hypot.f64 a2 a1)

rewrite67.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

281×	`times-frac_binary64`
174×	`add-sqr-sqrt_binary64`
158×	`*-un-lft-identity_binary64`
158×	`add-cube-cbrt_binary64`
76×	`sqrt-prod_binary64`

Counts

4 → 262

Calls

4 calls:

23.0ms	(*.f64 (cos.f64 th) (pow.f64 (/.f64 (hypot.f64 a2 a1) (/.f64 (sqrt.f64 2) (hypot.f64 a2 a1))) 1))
6.0ms	(/.f64 (hypot.f64 a2 a1) (/.f64 (sqrt.f64 2) (hypot.f64 a2 a1)))
3.0ms	(/.f64 (sqrt.f64 2) (hypot.f64 a2 a1))
0.0ms	(hypot.f64 a2 a1)

simplify262.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

433×	`fma-def_binary64`
321×	`associate-r_binary64`
298×	`associate-l_binary64`
255×	`associate-/l*_binary64`
238×	`associate-/r/_binary64`

Counts

370 → 444

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	479	9554
1	1110	8809
2	4291	8616
3	4973	8616
4	4961	8616

prune484.0ms (4.1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	484	2	486
Fresh	2	4	6
Picked	1	0	1
Done	0	1	1
Total	487	7	494

Error

Counts

494 → 7

Alt Table

Status	Error	Program
	15.8b	(.f64 (sqrt.f64 (cos.f64 th)) (.f64 (sqrt.f64 (cos.f64 th)) (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 2))))
	0.6b	(.f64 (cos.f64 th) (.f64 (/.f64 (hypot.f64 a2 a1) (sqrt.f64 (sqrt.f64 2))) (/.f64 (hypot.f64 a2 a1) (sqrt.f64 (sqrt.f64 2)))))
	0.8b	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 (sqrt.f64 2))) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2))))
✓	0.4b	(.f64 (cos.f64 th) (.f64 (/.f64 (hypot.f64 a2 a1) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (/.f64 (hypot.f64 a2 a1) (cbrt.f64 (sqrt.f64 2)))))
	0.9b	(.f64 (cos.f64 th) (pow.f64 (/.f64 (hypot.f64 a2 a1) (sqrt.f64 (/.f64 2 (fma.f64 a1 a1 (.f64 a2 a2))))) 1))
	0.7b	(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))
▶	0.5b	(.f64 (.f64 (cos.f64 th) (hypot.f64 a2 a1)) (pow.f64 (/.f64 1 (/.f64 (sqrt.f64 2) (hypot.f64 a2 a1))) 1))

Compiler

Compiled 13682 to 7260 computations (46.9% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 (cos.f64 th) (hypot.f64 a2 a1))
✓	0.3b	(/.f64 1 (/.f64 (sqrt.f64 2) (hypot.f64 a2 a1)))
✓	0.3b	(.f64 (.f64 (cos.f64 th) (hypot.f64 a2 a1)) (pow.f64 (/.f64 1 (/.f64 (sqrt.f64 2) (hypot.f64 a2 a1))) 1))
	0.5b	(/.f64 (sqrt.f64 2) (hypot.f64 a2 a1))

series183.0ms (1.6%)

Counts

3 → 96

Calls

3 calls:

120.0ms	(.f64 (.f64 (cos.f64 th) (hypot.f64 a2 a1)) (pow.f64 (/.f64 1 (/.f64 (sqrt.f64 2) (hypot.f64 a2 a1))) 1))
39.0ms	(*.f64 (cos.f64 th) (hypot.f64 a2 a1))
24.0ms	(/.f64 1 (/.f64 (sqrt.f64 2) (hypot.f64 a2 a1)))

rewrite66.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

258×	`times-frac_binary64`
145×	`add-sqr-sqrt_binary64`
143×	`*-un-lft-identity_binary64`
143×	`add-cube-cbrt_binary64`
78×	`associate-r_binary64`

Counts

3 → 242

Calls

3 calls:

22.0ms	(.f64 (.f64 (cos.f64 th) (hypot.f64 a2 a1)) (pow.f64 (/.f64 1 (/.f64 (sqrt.f64 2) (hypot.f64 a2 a1))) 1))
8.0ms	(/.f64 1 (/.f64 (sqrt.f64 2) (hypot.f64 a2 a1)))
3.0ms	(*.f64 (cos.f64 th) (hypot.f64 a2 a1))

simplify239.0ms (2%)

Algorithm

1×	egg-herbie

Rules

514×	`fma-def_binary64`
382×	`associate-l_binary64`
359×	`associate-r_binary64`
299×	`cancel-sign-sub-inv_binary64`
230×	`fma-neg_binary64`

Counts

338 → 417

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	367	8507
1	909	7560
2	3348	7422
3	4853	7422
4	4975	7422

prune496.0ms (4.3%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	492	0	492
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	492	7	499

Error

Counts

499 → 7

Alt Table

Status	Error	Program
	15.8b	(.f64 (sqrt.f64 (cos.f64 th)) (.f64 (sqrt.f64 (cos.f64 th)) (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 2))))
	0.6b	(.f64 (cos.f64 th) (.f64 (/.f64 (hypot.f64 a2 a1) (sqrt.f64 (sqrt.f64 2))) (/.f64 (hypot.f64 a2 a1) (sqrt.f64 (sqrt.f64 2)))))
	0.8b	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 (sqrt.f64 2))) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2))))
✓	0.4b	(.f64 (cos.f64 th) (.f64 (/.f64 (hypot.f64 a2 a1) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (/.f64 (hypot.f64 a2 a1) (cbrt.f64 (sqrt.f64 2)))))
	0.9b	(.f64 (cos.f64 th) (pow.f64 (/.f64 (hypot.f64 a2 a1) (sqrt.f64 (/.f64 2 (fma.f64 a1 a1 (.f64 a2 a2))))) 1))
	0.7b	(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))
✓	0.5b	(.f64 (.f64 (cos.f64 th) (hypot.f64 a2 a1)) (pow.f64 (/.f64 1 (/.f64 (sqrt.f64 2) (hypot.f64 a2 a1))) 1))

Compiler

Compiled 14331 to 8148 computations (43.1% saved)

regimes2.1s (18%)

Accuracy

Total 0.4b remaining (95.2%)

Threshold costs 0.4b (95.2%)

Counts

219 → 1

Compiler

Compiled 38776 to 26913 computations (30.6% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	36
1	16	36
2	16	36

end138.0ms (1.2%)

Remove: (sort a1 a2)
Compiler: Compiled 249 to 180 computations (27.7% saved)

Details

analyze1.2s (10.5%)

sample4.8s (41.5%)

simplify9.0ms (0.1%)

prune4.0ms (0%)

localize9.0ms (0.1%)

series94.0ms (0.8%)

rewrite17.0ms (0.1%)

simplify111.0ms (1%)

prune147.0ms (1.3%)

localize11.0ms (0.1%)

series300.0ms (2.6%)

rewrite59.0ms (0.5%)

simplify187.0ms (1.6%)

prune382.0ms (3.3%)

localize11.0ms (0.1%)

series213.0ms (1.8%)

rewrite67.0ms (0.6%)

simplify262.0ms (2.2%)

prune484.0ms (4.1%)

localize11.0ms (0.1%)

series183.0ms (1.6%)

rewrite66.0ms (0.6%)

simplify239.0ms (2%)

prune496.0ms (4.3%)

regimes2.1s (18%)

simplify3.0ms (0%)

end138.0ms (1.2%)

Profiling